Question Number 193714 by Rupesh123 last updated on 18/Jun/23
Commented by Frix last updated on 18/Jun/23
$$\sqrt{\mathrm{17}\pm\sqrt{\mathrm{288}}}=\sqrt{\mathrm{17}\pm\mathrm{12}\sqrt{\mathrm{2}}}=\mathrm{3}\pm\mathrm{2}\sqrt{\mathrm{2}} \\ $$$$\sqrt{\mathrm{7}\pm\sqrt{\mathrm{48}}}=\sqrt{\mathrm{7}\pm\mathrm{4}\sqrt{\mathrm{3}}}=\mathrm{2}\pm\sqrt{\mathrm{3}} \\ $$$$\Rightarrow \\ $$$$\mathrm{Answer}\:\mathrm{is}\:\mathrm{2} \\ $$
Commented by Mingma last updated on 18/Jun/23
Perfect ��
Commented by Rupesh123 last updated on 18/Jun/23
Perfect ��
Answered by AST last updated on 18/Jun/23
$${a}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{34},{ac}=\mathrm{1}\Rightarrow\left({a}+{c}\right)^{\mathrm{2}} −\mathrm{2}{ac}=\mathrm{34}\Rightarrow{a}+{c}=\mathrm{6} \\ $$$${b}^{\mathrm{2}} +{d}^{\mathrm{2}} =\mathrm{14},{bd}=\mathrm{1}\Rightarrow\left({b}+{d}\right)^{\mathrm{2}} −\mathrm{2}{bd}=\mathrm{14}\Rightarrow{b}+{d}=\mathrm{4} \\ $$$$\Rightarrow{a}−{b}+{c}−{d}=\mathrm{2} \\ $$
Commented by Mingma last updated on 18/Jun/23
Perfect ��
Commented by Rupesh123 last updated on 18/Jun/23
Perfect ��